Problem: Simplify the following expression: $ r = \dfrac{-2}{7} + \dfrac{5}{-5p - 1} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5p - 1}{-5p - 1}$ $ \dfrac{-2}{7} \times \dfrac{-5p - 1}{-5p - 1} = \dfrac{10p + 2}{-35p - 7} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{5}{-5p - 1} \times \dfrac{7}{7} = \dfrac{35}{-35p - 7} $ Therefore $ r = \dfrac{10p + 2}{-35p - 7} + \dfrac{35}{-35p - 7} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{10p + 2 + 35}{-35p - 7} $ $r = \dfrac{10p + 37}{-35p - 7}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{-10p - 37}{35p + 7}$